6. the sun of the digits of a certain two digit number is 6. if the original number is subtracted from the number formed by interchanging the digits, the result is 36. find the original number

Answer:

3239609472 Km

Step-by-step explanation:

Answer: One Half

Step-by-step explanation: 3 is half of 6 and  I took the test ;)

Yes, it is widely known that 100-200 high-frequency words account for about 50% of the words used in school texts. This highlights the importance of explicitly teaching these words to students in order to improve their reading fluency and comprehension.

Among these high-frequency words, almost 25% are permanently irregular, meaning that they do not follow standard spelling and pronunciation rules. This makes it even more important for students to learn these words through direct and systematic instruction, as they can greatly impact their reading and writing abilities. By focusing on these high-frequency words, educators can help students build a strong foundation of vocabulary knowledge, which can lead to improved reading outcomes and success in school.

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If you draw 2 cards, the probability of drawing 1 heart and 1 non-heart card are: 26/676.

It's crucial to keep in mind that your chances may change depending on the particular rules of the card game you're playing. B. The quantity of cards in the deck, the number of cards drawn, and whether or not the cards drawn after play were replaced.

A regular deck of 52 cards has a chance of producing exactly one heart depending on how many cards are drawn.

The likelihood of drawing a heart if you only draw one card is 13/52, or 1/4.

The probabilities of getting a card with a heart and a non-heart are:

(13/52) × (39/51) + (39/52) × (13/51) = 26/676

And if more cards are drawn, the odds of drawing exactly one heart are different.

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The value of x is equal to 16

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².

Given here: A right angle triangle

let the triangle be ABC with AC as the hypotenuse and AB is the perpendicular and BC is the base of the triangle. And D be a point on AC with AD=32 and DC=8 .Clearly the perpendicular using the pythagoras theorem

AB=[tex]\sqrt{x^2+32^2}[/tex]

Now in triangle BDC we have BC= [tex]\sqrt{x^2+64}[/tex]

Again a triangle ABC we have

AC²=BC²+AB²

[tex]40^2=x^2+64+x^2+32^2\\2x^2=40^2-32^2-64\\2x^2=512\\x^2=256\\x=16[/tex]

Thus x is equal to 16

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An equation for the total cost, y, in terms of the number of kites purchased, x, is y = 2x + 20.

In order to write a linear equation to describe this situation, we would a assign variable to the number of kites purchased and the total cost respectively, and then translate the word problem into a linear equation as follows:

Since Wendy charges $2 per kite and a flat rate of $20 for shipping, a linear equation that models the total cost is given by:

y = 2x + 20

When x = 4, the total cost for Wendy kites is given by:

y = 2(4) + 20

y = $28.

When x = 7, the total cost for Wendy kites is given by:

y = 2(7) + 20

y = $34.

When x = 10, the total cost for Wendy kites is given by:

y = 2(10) + 20

y = $40.

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If twice Brittany's age is less than the age of Abraham Lincoln when he died, then the answers are;

2b < 56

n = b - 2

b = n + 2

b < 28

n = b - 2 < 26

Yes, Brittany could be 27 years old and Nate 26

Let Brittany's age = b

Twice Brittany's age = 2 × b = 2b

Lincoln's age = 56

Inequality to represent Brittany's age: 2b < 56

b < 56/2 = 28

Nate's age = n

in terms of Brittany's age: n = b - 2

Isolating b: b = n + 2

Substituting b: b < 28

Solving for b: b < 28 and n = b - 2 < 26

Could Brittany be 27 years old and Nate 26? Yes, Brittany could be 27 years old and Nate 26 as both are within the range defined by the inequality (b < 28 and n < 26).

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The complete question is:

Twice Brittany’s age is less than the age of Abraham Lincoln when he died. President Lincoln was 56 years old at the time of his death. Write an inequality to represent Brittany’s age, b. Brittany’s brother, Nate, is two years younger than Brittany. Write an equation for Nate’s age, n, in terms of Brittany’s age, b. Rewrite the expression from Part B to get the variable b alone on one side of the equation. (This is also called isolating b.) Substitute the value of b from Part C into the inequality you found in Part A. Solve the inequalities from parts A and D for the variables b and n, respectively. Could Brittany be 27 years old and Nate 26? Why or why not?

The value of {x} is equivalent to {x} = 4β - (y + z).

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that triangle and the square have equal perimeters.

Assume the lengths of the triangle are {x}, {y} and {z} respectively.

Let the side length of a square be β. We can write -

P{T} = P{S}

(x + y + z) = 4β

{x} = 4β - (y + z)

Therefore, the value of {x} is equivalent to {x} = 4β - (y + z).

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The option that would give the most money after 2 years would be Option 1.

The amount that Option 1 would give after 2 years is:

= Amount invested x ( 1 + rate / number of periods ) ^ number of periods in quarters

= 1, 000 x ( 1 + 12 % / 4 ) ⁴ ˣ ²

= $ 1, 267

The amount Option 2 would give after 2 years with continuous compounding is:

= Amount to invest x e ^ ( rate  x number of periods)

= 1, 000 x e ^ ( 6 % x 2 years )

= $1, 127 .50

Option 1 is the better option.

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Answer:

Hi Elm!

Step-by-step explanation:

In a polygon, the sum of the measures of the interior angles and the sum of the measures of the exterior angles of adjacent angles are related. Specifically, the sum of the measures of the interior angles of a polygon is equal to (n - 2) times 180 degrees, where n is the number of sides in the polygon. For a given interior angle and its adjacent exterior angle, the measure of the exterior angle is equal to the sum of the interior angle and 180 degrees.

Step-by-step explanation:

I hope this helps a bunch! Make sure to rephrase!

6. The costs are given as follows:

7. The linear function is defined as follows:

y = 20 + 2x.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the table, when x = 0, y = 20, hence the intercept b is given as follows:

b = 20.

When x increases by one, y increases by two, hence the slope m is given as follows:

m = 2.

Then the function giving the cost y of x kites is defined as follows:

y = 2x + 20.

The costs are given obtaining the numeric values, replacing the lone instance of x in the equation by the number of kites, thus:

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The angle of elevation of the observer to the kite is around 30 degrees

The hypotenuse in the given question is 405 feet, while the height of the kite from the ground is 210 feet.

It is also stated that the kite's height from the ground does not change.

The tangent function may be used to calculate the angle of elevation.

tan(angle of elevation) = height of the kite / horizontal distance to the kite

Since the height of the kite is 210 feet and the horizontal distance (the length of the kite string) is 405 feet, we can calculate the angle of elevation:

Let Ф be the angle of elevation

tan(angle of elevation) = 210/405

Ф = tan-1(210/405)

Ф = tan-1(0.516)

Ф = roughly 30 degrees

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The value of the standard deviation depends on the value of the mean.

As per the given data, we have to determine that the value of the standard deviation depends on the value of the mean

Yes, the value of the standard deviation depends on the value of the mean.

Because you have to know the mean to calculate the standard deviation.

The size of the standard deviation of a data set depends on what the mean is because the calculation of the mean is essential for calculating Standard Deviation.

The standard deviation determines how much the values deviate from the mean.

Besides, Standard deviation in simple terms means the deviation of data from the Mean.

The most popular way to assess dispersion is standard deviation, which is based on all values. As a result, even a small change in one value can modify the standard deviation's value.

Hence, Standard Deviation depends on the Mean.

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A graph of the solution (4, 4) for the system of linear equations is shown in the image attached below.

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

In this context, we would replace the y-value of the first equation 4x - 2y = 8 with zero (0) as follows;

4x - 2(0) = 8

4x = 8

x = 2 ⇒ (2, 0).

For the y-intercept of the first equation 4x - 2y = 8, we would substitute the x-value with zero (0) as follows;

4(0) - 2y = 8

2y = -8

y = -4 ⇒ (0, -4).

For the y-intercept of the first equation y = 3x/2 - 2, we would substitute the x-value with zero (0) as follows;

y = 3(0)/2 - 2

y = -2 ⇒ (0, -2).

Based on the graph shown in the image attached below, we can logically deduce that the solution to this system of linear equations is at the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is equal to the ordered pair (4, 4).

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Answer:

Similar by AA/SAS

Step-by-step explanation:

20.8/8 = 23.4/9 = 2.6

So, the bottom of the smaller triangle is parallel the bottom of the larger one (Thales' theorem)

So, corresponding angles are equal and hence, they are similar by AA similarity.

Note: As sides are given, similarity can also be proven by SAS.

The correct option for the true proportion is  AB/EF = CD/GH (option D)

Two figures are called similar if they have equal corresponding angles and their side are in same  ratios,

Given that, there are two similar polygons, ABCD and EFGH, we need to find the true proportion for the side of the polygons,

We know that, similar figure have equal ratios of the corresponding sides,

Therefore, we get,

AB/EF = CD/GH = BC/FG = AD/EH

From the options given, the true proportion is

AB/EF = CD/GH (option D)

Hence, the correct option for the true proportion is  AB/EF = CD/GH (option D)

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The total distance covered while swimming and running for a total of 3 hours is 45 kilometers.

In mathematics, the term "total" refers to the sum of two or more values. It is used to describe the combined or complete amount of a quantity. The total can be calculated by adding together all the individual values in a set or series.

The distance x can be calculated by using the formula:

distance = rate * time

For swimming, the rate is 5 kilometers per hour, and the time is t₁. So, the distance covered while swimming is:

d₁ = 5 * t₁

For running, the rate is 20 kilometers per hour, and the time is t2. So, the distance covered while running is:

d₂ = 20 * t2

The total time for swimming and running is 3 hours, so:

t₁ + t₂ = 3

The total distance covered while swimming and running is x, so:

x = d₁ + d₂

Substituting the values of d₁ and d₂, we get:

x = 5 * t₁ + 20 * t₂

Now, substituting the value of t₁ + t₂ = 3, we get:

x = 5 * t₁ + 20 * (3 - t₁)

Expanding the equation, we get:

x = 5 * t₁ + 60 - 20 * t₁

Combining the like terms, we get:

x = -15 * t₁ + 60

Substituting the value of t₁ = 3 - t2, we get:

x = -15 * (3 - t2) + 60

Expanding the equation, we get:

x = 45 - 15 * t₂

Now, we have to find the value of t₂ such that x is maximum.

Taking the derivative of x with respect to t₂, we get:

dx/dt₂ = -15

So, t₂ is a decreasing function of x. Hence, when t₂ is maximum, x is also maximum.

As t₂ cannot be negative, the maximum value of t₂ is 0. Hence,

t₂ = 0

Substituting the value of t₂ = 0 in the equation x = 45 - 15 * t₂, we get:

x = 45

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Let x represent the number of chickens and y represent the number of sheep.There is no proper system equation so such farms does not exist as this equations contradict.

A system of equations is a set of multiple equations with multiple variables that are related to each other. It is a mathematical problem that requires a solution for each equation in the system.

The total number of legs on the farm is given as "4x + 2y". What's more, we are told that the total number of animals is "x + y".

4x + 2y means the total legs

x + y = the number of total of animals

We'll now use the Elimination method to identify x and y.

One method is to multiply the first equation by 2 and subtract it from the second:

(2) * legs = (4x + 2y)

2x + 2y = the total number of animals

Legs = (2x + 2y)

0 = number of legs - 2 * the amount of animals

When we solve for the number of animals we get:

animal count = legs / 2

So, if we connect this back into either equation, we can find x and y.

Let's look at the first equation:

4x + 2y means the total legs

legs / 2 = x + y

When we substitute legs / 2 in the second equation for "number of animals," we get:

legs / 2 = x + y

Now we'll use substitution to find x. In the first equation, we'll substitute x = legs / 2 - y:

4x + 2y means the total legs

legs = 4(legs / 2 - y) + 2y

legs = 2 * legs - 4y + 2y

2 times legs = legs

There are no solutions due to this contradiction, and no such farm exists under the given conditions.

As a result, the answer to the system of equations is that no such farm occurs under the given conditions.

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The first three triangles are similar triangles as their corresponding sides are in same proportion but the last triangle with side lengths 4, 6, and 8 does not belong to the first three.

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

The base lengths 12, 6, and 18 of the first three triangles corresponds in proportion but does not for the last triangle with 8.

The side 6, 3, and 9 corresponds in proportion but does not for the side 4 of the last triangle

And lastly, the side 8, 4, and 12 of the first three triangles corresponds in proportion but does not for the last triangle with side length 6.

Therefore, the first three triangles are similar triangles as their corresponding sides are in same proportion but the last triangle with side lengths 4, 6, and 8 does not belong to the first three.

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Answer:

6 1/2

Step-by-step explanation:

The difference between 13 9/20 and 6 7/8 can be found by converting both fractions to decimals and subtracting the two values.

13 9/20 can be expressed as a decimal as 13.45.

6 7/8 can be expressed as a decimal as 6.875.

So, the difference between 13 9/20 and 6 7/8 can be expressed as:

13.45 - 6.875 = 6.575

So the reasonable difference between 13 9/20 and 6 7/8 is 6.575.

So y = 2x + 2 is the equation of a line parallel to line ef and includes point (0, 2).

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign.

Here,

Since line ef has a slope of 2, any line parallel to it will also have a slope of 2. The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. To find an equation of a line parallel to line ef that contains point (0, 2), we need to find its y-intercept.

We can use the point-slope form of a line to find the equation of the line: y - y1 = m(x - x1)

Plugging in the point (0, 2) and the slope of 2, we get:

y - 2 = 2(x - 0)

y - 2 = 2x

y = 2x + 2

So, the equation of a line parallel to line ef and containing point (0, 2) is y = 2x + 2.

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The coordinates of A', B', C' and D' are obtained as follows:

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

Hence the coordinates of the dilated figure are obtained multiplying it's respective coordinates on the original figure by the scale factor.

The problem is incomplete, hence the answer was given in general terms.

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Zeke's average speed in mph for the first 20 minutes was 3 mph.

To find Zeke's average speed in mph for the first 20 minutes, divide the distance traveled by the time it took him to travel that distance:

1.0 mile / 20 minutes = 0.05 miles per minute

Since there are 60 minutes in an hour, to convert minutes per mile to miles per hour, multiply by 60:

0.05 miles per minute * 60 minutes per hour = 3 mph

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The value of x that makes ABC~ ADEF is 4

From the question, we have the following parameters that can be used in our computation:

AABC~ ADEF.

So, we have the following equivalent ratio

6 : 2x = 24 : 32

So, we have

2x/6 = 32/24

Make x the subject

So, we have the following representation

x = 6 * 32/(24 * 2)

Evaluate the expression

x = 4

Hence, the value is 4

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Answer:

as 92 is 2 std deviaiton above mean ; th

Step-by-step expla

The given expression 5 subtracted from three times any number is written as 3x - 5

Algebra is the system of computation using letters or other symbols to represent numbers.

5 subtracted from three times any number.

Let

the unknown number= x

(3 × x) - 5

= 3x - 5

Therefore, 3x - 5 is the algebraic representation of the expression.

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The standard deviation represents the variability or spread of the data when graphing the class average for the serial dilution experiment.

It shows how much the individual data points deviate from the mean, or average, of the class data. The standard deviation can be used to determine how much variation there is in the data and how much the data is spread out from the mean.

If the standard deviation is small, it means that the data points are very close to the mean, and if the standard deviation is large, it means that the data points are spread out over a larger range.

The standard deviation is important to consider when analyzing data in the serial dilution experiment, as it gives insight into the variability of the data and helps to determine if the data is accurately representing the experiment.

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Answer:

Step-by-step explanation:

15+.31x ≤ 93

Answer:

Below

Step-by-step explanation:

Volume of a cylinder :    Find the area of the end....then multiply by height

Volume = pi r^2     *   h

                 3.14 (6)^2  mm)   *  6 mm = 678.24 mm^3

Step-by-step explanation:

[tex]3x - \frac{8}{2} = x - 6[/tex]

[tex] \frac{8}{2} = 4[/tex]

[tex]3x - 4 + 4 = x - 6 + 4[/tex]

[tex]3x = x - 6 + 4[/tex]

[tex]3x - x = - 6 + 4 - x[/tex]

[tex]3x - x = - 6 + 4[/tex]

[tex]2x = - 2[/tex]

[tex] \frac{2x}{2} = \frac{ - 2}{2} [/tex]

[tex]x = - 1[/tex]